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Standard XII
Mathematics
Definition of Relations
A relation wh...
Question
A relation which satisfies reflexive symmetric and transitive is ________ relation
A
an identity
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B
a constant
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C
an equivalence
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D
None of these
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Solution
The correct option is
C
an equivalence
A relation which satisfies reflexive symmetric and transitive is _called an equivalence relation
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Similar questions
Q.
If
R
is an equivalence relation on a set
A
, then
R
−
1
is
Q.
Since an object is identical with itself 'being identicaly, is called a reflexive relation and if a relation is transitive, symmetric and reflexive, then such a relation is called 'equivalence'. If so, what kind of relation is "different"?
Q.
Let
A
=
{
1
,
2
,
3
}
and
R
,
S
be two relations on
A
given by
R
=
{
(
1
,
1
)
,
(
2
,
2
)
,
(
3
,
3
)
,
(
1
,
2
)
,
(
2
,
1
)
}
,
S
=
{
(
1
,
1
)
,
(
2
,
2
)
,
(
3
,
3
)
,
(
2
,
3
)
,
(
3
,
2
)
}
then
R
∪
S
is
Q.
Give an example of a relation. which is reflexive and symmetric and Transitive
Q.
Let
R
=
{
(
3
,
3
)
,
(
6
,
6
)
,
(
9
,
9
)
,
(
12
,
12
)
,
(
6
,
12
)
,
(
3
,
9
)
,
(
3
,
12
)
,
(
3
,
6
)
}
be a relation on the set
A
=
{
3
,
6
,
9
,
12
}
.
Then the relation is
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